The problem concerning the flexure of a cylindrical shell due to a radial concentrated force

1967 ◽  
Vol 3 (6) ◽  
pp. 77-79 ◽  
Author(s):  
Yu. P. Zhigalko
Keyword(s):  
Cylindrical Shell ◽  
Concentrated Force

Correlation Parameters for Eliminating the Effect of Pulse Shape on Dynamic Plastic Deformation

1970 ◽  
Vol 37 (3) ◽  
pp. 744-752 ◽  
Author(s):  
C. K. Youngdahl
Keyword(s):  
Plastic Deformation ◽  
Cylindrical Shell ◽  
Pulse Shape ◽  
Circular Cylindrical Shell ◽  
Strong Dependence ◽  
Uniform Pressure ◽  
Concentrated Force ◽  
Total Impulse ◽  
The Mean ◽  
Mean Time

The solutions to four classical problems in dynamic plasticity—the circular plate under uniform pressure, the reinforced circular cylindrical shell under uniform pressure, the free-free beam with a central concentrated force, and the circular cylindrical shell with a ring load—are examined to determine the effect of pulse shape on final plastic deformation. It is found that there is a strong dependence on pulse shape for pulses which have the same total impulse and maximum load; however, the effect of the pulse shape is virtually eliminated if the pulses have the same total impulse and “effective load.” The “effective load” is defined as the impulse divided by twice the mean time of the pulse, where the mean time is the interval between the onset of plastic deformation and the centroid of the pulse.

Application of Short and Long (Enhanced Vlasov's) Solutions for Cylindrical Shell on Example of Concentrated Radial Force

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Andrii Oryniak ◽  
Igor Orynyak
Keyword(s):  
Cylindrical Shell ◽  
Efficient Solution ◽  
Radial Force ◽  
Circumferential Direction ◽  
Axial Line ◽  
Eighth Order ◽  
Concentrated Force ◽  
Accuracy Of Results ◽  
Analytical Approaches ◽  
Asme Paper

Abstract Analytical approaches for cylindrical shell are mostly based on expansion of all variables in Fourier series in circumferential direction. This leads to eighth-order differential equation with respect to axial coordinate. Here it is approximately treated as a sum of two fourth-order biquadratic equations. First one assumes that all variables change more quickly in circumferential direction than in axial one (long solution), while the second (short) one is based on opposite assumption. The accuracy and applicability of this approach were demonstrated (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032) on example of action of one or two concentrated radial forces and compared with finite element method results. This paper is an improvement of our previous work (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032). Two amendments are made. The first is insignificant one and use slightly modified expressions for bending strains, while the second one relates to the short solution. Here we do not consider any more that circumferential displacement is negligible as compared with radial one. Eventually this improves the accuracy of results, as compared with previous work. For example, for cylinder with radius, R, to wall thickness, h, ratio equal to 20, the maximal inaccuracy for radial displacement in point of force application decreases from 5% to 3%. For thinner cylinder with R/h = 100, this inaccuracy decreases from 2.5% to 1.25%. These inaccuracies are related to larger terms in Fourier expansion, the significance of which decrease when length or area of outer loading becomes greater. The last conclusion is demonstrated for the case of distributed concentrated force acting along short segment on axial line.

scholarly journals Application of exponential functions in weighted residuals method in structural mechanics. Part 3: infinite cylindrical shell under concentrated forces

2021 ◽  
Vol 5 (2) ◽  
pp. 165-176
Author(s):  
Igor Orynyak ◽  
Yulia Bai ◽  
Anastasiia Hryhorenko
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Fundamental Problem ◽  
Weighted Residual Method ◽  
Exponential Functions ◽  
Analytical Treatment ◽  
Concentrated Force ◽  
Exact Relation ◽  
Analytical Technique ◽  
Weighted Residuals

Solution for cylindrical shell under concentrated force is a fundamental problem which allow to consider many other cases of loading and geometries. Existing solutions were based on simplified assumptions, and the ranges of accuracy of them still remains unknown. The common idea is the expansion of them into Fourier series with respect to circumferential coordinate. This reduces the problem to 8th order even differential equation as to axial coordinate. Yet the finding of relevant 8 eigenfunctions and exact relation of 8 constant of integrations with boundary conditions are still beyond the possibilities of analytical treatment. In this paper we apply the decaying exponential functions in Galerkin-like version of weighted residual method to above-mentioned 8th order equation. So, we construct the sets of basic functions each to satisfy boundary conditions as well as axial and circumferential equilibrium equations. The latter gives interdependencies between the coefficients of circumferential and axial displacements with the radial ones. As to radial equilibrium, it is satisfied only approximately by minimizations of residuals. In similar way we developed technique for application of Navier like version of WRM. The results and peculiarities of WRM application are discussed in details for cos2j concentrated loading, which methodologically is the most complicated case, because it embraces the longest distance over the cylinder. The solution for it clearly exhibits two types of behaviors – long-wave and short-wave ones, the analytical technique of treatment of them was developed by first author elsewhere, and here was successfully compared. This example demonstrates the superior accuracy of two semi analytical WRM methods. It was shown that Navier method while being simpler in realization still requires much more (at least by two orders) terms than exponential functions.

Vibration and acoustic radiation of an orthotropic composite cylindrical shell in a hygroscopic environment

2016 ◽  
Vol 23 (4) ◽  
pp. 673-692 ◽  
Author(s):  
Xin Zhao ◽  
Bo Zhang ◽  
Yueming Li
Keyword(s):  
Cylindrical Shell ◽  
Moisture Content ◽  
Acoustic Radiation ◽  
Radiation Power ◽  
Orthotropic Cylindrical Shell ◽  
Sound Radiation ◽  
Composite Cylindrical Shell ◽  
Buckling Mode ◽  
Concentrated Force ◽  
Orthotropic Composite

An analytical study is presented for vibration and acoustic radiation of a finite thin orthotropic composite cylindrical shell excited by a harmonic concentrated force in a hygroscopic environment. The modal analysis method is used to solve the governing equations. Theoretical results are presented in natural vibration, radial quadratic velocity, sound power and radiation efficiency, with uniform incremental moisture content. Furthermore, different stiffness, length and thickness are set respectively to research the effects of the material and structure parameters variation of the orthotropic cylindrical shell on the vibration and acoustic radiation characteristics. It is found that the natural frequencies decrease with an increase of moisture content. The modal indices associated with the lowest frequency mode reaches the modal indices corresponding to the lowest buckling mode near the critical buckling moisture content with moisture content. The radial quadratic velocity and sound radiation power decrease with the incremental moisture content in the lower frequency band. The vibration and acoustic response decrease with the enhanced stiffness. The increasing length has little impact on the sound radiation and the thickened cylindrical shell weakens the sound radiation response.

Elasto-plastic state of curve beam system subjected to complex loading

1996 ◽  
Vol 18 (4) ◽  
pp. 14-22
Author(s):  
Vu Khac Bay
Keyword(s):  
Cylindrical Shell ◽  
Solution Method ◽  
Complex Loading ◽  
Numerical Results ◽  
Elastic Solution ◽  
Plastic State ◽  
Curve Beam ◽  
Elastic State ◽  
Elastic Plastic ◽  
Beam System

Investigation of the elastic state of curve beam system had been considered in [3]. In this paper the elastic-plastic state of curve beam system in the form of cylindrical shell is analyzed by the elastic solution method. Numerical results of the problem and conclusion are given.

Dynamic stability of a free-free cylindrical shell under a follower force

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1070-1077
Author(s):  
Si-Hyoung Park ◽  
Ji-Hwan Kim
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Follower Force
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